A finite set covering theorem III

E-ISSN： 1755-1633|6|3|417-433

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.6, Iss.3, 1972-06, pp. : 417-433

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Abstract

Let n, s, t be integers with s > t > 2. If a family of n different subsets of a set S, with s elements, has the properties,(i) each member belongs to a set of (t+1) members which together have union S,(ii) no member belongs to a set of t members which together have union S,then we prove that n ≤ (t+1)^s−t−1. The result is best possible.

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